Topic #13 . Gas Laws

Topic #13. Gas Laws

1. Kinetic Theory

2. Pressure

3. Boyle's Law

4. Charles' Law

5. Gay-Lussac's Law

6. Combined Gas Law

7. Ideal Gas Law

8. Real Gases

Notes should include:

Kinetic Theory: Whenever you study the properties of material substances, you will get into discussing what matter is made of, and how its structure varies among the different phases of matter, solid, liquid, and gas. The core principle in the study of matter and thus the nature of materials is the kinetic theory. The kinetic theory provides us with an explanation of how the particles that make up a substance behave. This is a valuable concept when studying gases. A number of sources tell you that the kinetic theory is based on three assumptions. They are:

1. Matter, regardless of type or form, is made up of very small particles.

2. These particles are constantly in motion, and generally this motion is random.

3. The particles themselves experience collisions with other particles and often with the

walls of a container, if confined to one. These collisions are considered to be elastic.

The kinetic theory applies to gases. When studying gases, particularly in a first course in physics, you generally consider an ideal gas. An ideal gas is a hypothetical gas made up of particles having mass, but no significant volume. Also the particles in the ideal gas exhibit no amount of attractive force for each other or the sides of containers, if so confined.

Pressure: The study of gases requires that you find a means of measuring quantities of gaseous material other than those commonly used for measuring quantities of materials in either the liquid or solid state. It isn't convenient to simply lay some gas on a balance to mass it or pore some into a graduate cylinder to find its volume. As a consequence, the measurements of Pressure, Temperature, and Volume are used together to describe the quantity of a gas present in a particular situation. You are more likely to be familiar with temperature and volume than you are with the measurement of pressure, though you may have used a pressure gauge in the past for the purpose of checking the pressure of something such as a bicycle tire. Pressure is the measure of the force exerted by the particles of a gas acting on, pressing against, or colliding with one unit area of measure on the surface of a container in which the gas is confined. For example, Pressure is often expressed in PSI, which stands for pounds per square inch. Notice that the phrase per square inch is one unit area of measurement. The SI unit for pressure is the pascal, abbreviated Pa. A pascal is equal to one newton per square meter. 1 Pa = 1 N/m2.

You will often see pressure expressed in kilopascals (kPa), because one pascal is a rather small measurement.

A barometer is a device used to measure atmospheric pressure. You should always remember that the weight of the atmosphere is pressing down on you and everything else on the earth's surface. This weight is the pressure of the atmosphere. On the average the atmospheric pressure near the surface of the earth is 14.7 psi. As with most measurements, pressure requires that there be some standard reference point or measurement to which (or upon which) all other measurements are compared (or defined). When working with pressure you refer to standard atmospheric pressure. Standard atmospheric pressure is defined as the amount of pressure exerted by the atmosphere that will support a column of mercury that is 760 mm above the pool of mercury in a barometer. This measurement is reported as 760 mm Hg. Expressed in pascals this would be 1.013 x 105 Pa or in kilopascals 101.3 kPa. The aneroid barometer, which often looks like a round pressure gauge, works by monitoring the effect atmospheric pressure has on a small chamber from which most, if not all, of the air has been removed. A mechanical linkage that monitors the change in volume of this chamber as the atmospheric pressure changes moves the needle that sits on the numbered scale, thus allowing you to read the atmospheric pressure right off the face of this type of barometer.

Boyles' Law: Back in the 17th century, a British scientist by the name of Robert Boyle discovered the relationship between the pressure and the volume of a gas. This relationship has become well known to chemistry and physics students as Boyle's Law. His law says that the volume of a gas varies inversely with the pressure of the gas, if the temperature of the gas remains constant. The equation for this law can be written as Pi Vi = Pf Vf. (i = initial measurement and f = final measurement) The relationship can also be written as PV = C, where C represents a numerical constant. The letter k could also be used to represent the constant. If you were to graph the data that supports this law, you would get a first quadrant hyperbola.

Charles' Law: Near the end of the 18th century a scientist by the name of Jacques Charles discovered the relationship between temperature and the volume of a gas. This relationship has also become well known to chemistry and physics students. It is referred to as Charles' Law. This law says that the volume of a gas varies directly with the temperature of the gas, if the pressure of the gas remains constant. The equation for this law is Vi / Vf = Ti / Tf. If you were to graph data that supports this law, you would get a straight line.

Gay-Lussac's Law: In the early 19th century a scientist by the name of Joseph Gay-Lussac discovered the relationship between temperature and pressure. This law says that the pressure of a gas varies directly with the pressure of the gas, if the volume of the gas remains constant. The equation for this law is Pi / Pf = Ti / Tf. If you were to graph data that supports this law, you would get a straight line.

A noteworthy comment: Boyle's, Charles', and Gay-Lussac's laws are not really laws in the sense that we use the term law today. Rather, they are reasonable approximations that are considered correct for real gases as long as they are not too close to their condensation points and their pressures and densities are not very high. However, because calling these statements laws has a strong historical basis, we will continue to call them laws. Remember, for the purpose of learning relationships, we are tending to ignore the effect of attractive forces on the behavior of gases. We are treating them ideally, with certain limitations placed on the conditions under which we are studying them. One of those conditions involves completely elastic collisions.

Combined Gas Law: Since it is not always likely that one of the three variables of temperature, pressure, and volume will remain constant a relationship that allows for all three to change simultaneously is needed. This relationship is called the combined gas law. The equation for this law can be written as Pi Vi / Ti = Pf Vf / Tf. If you were to state this relationship in words, you could say that the product of the pressure and volume of a gas varies directly with its temperature.

Ideal Gas Law: Decreasing the volume and / or increasing the temperature of a gas are not the only means of affecting the pressure of a gas. Up until now we have ignored the effect that the number of particles has on the pressure of a gas. For example, consider the effect of adding more air (molecules) to a bicycle or automobile tire. As you do so, the pressure goes up. This happens because when the temperature and volume of a gas are held constant but the number of particles is increased the density of the gas increases causing more collisions in the same amount of space including collisions with the surface are of the wall of the container in which the gas is being held. This means that the pressure has increased, as the number of collisions against the wall per unit area represent a way of expressing the force pushing on that wall.

It can also be said that, if the temperature of a gas remains constant, the product of its pressure and volume varies directly with the number of molecules of gas present. A mathematician would write this relationship as PV a n , where n is the number of particles (molecules) present. The symbol "a" means "varies directly with". The number of particles are usually expressed using a unit called the mole. A mole of a substance is equal to 6.02 x 1023 particles or molecules. This rather large number is called Avogadro's number. For example, 0.5 moles of oxygen molecules equals 3.01 x 1023 molecules of oxygen. Likewise, 2.0 moles of carbon dioxide molecules equals 1.204 x 1024 molecules of carbon dioxide molecules.

[In the 19th century Amedeo Avogadro, an Italian scientist came up with the following hypothesis. He said "equal volumes of gases at the same pressure and temperature contain equal numbers of molecules". The term mole itself is defined as the amount of substance that contains as many atoms or molecules as there are in 0.012 kg of carbon - 12. Avogadro was not able to determine the actual number of particles in the mole during his lifetime. It required 20th century technology to do so. However, the idea is his, so to honor him, we name the number after him.]

Since the product PV is also varies directly with temperature, a more expansive relationship may be expressed that says the product of the pressure and volume for a gas varies directly with the product of its temperature and the amount of gas present. Mathematically this can be written as PV  nT. From this statement the mathematical relationship can be written in the form of a ratio that is equal to a numerical constant. This relationship can be expressed as PV / nT = k , where k is a numerical constant called the Boltzman's constant. The Boltzman's constant requires that the value for n be expressed in terms of the actual number of molecules of gas present. The relationship can also be expressed as PV / nT = R. The letter k is replaced with the letter R. In this situation the value for n is expressed in terms of the number of moles of gas present. The letter R is sometimes referred to as the universal (gas) constant. This equation is often rearranged and written as PV = nRT. This is the form of the equation is most often written to represent the ideal gas law. It allows you to work with four variables simultaneously.

[The value for R will depend upon what units you use for P, V, n, T. In high school chemistry books, R is often given as 0.082 L Atm / mol K. This requires that P be expressed in atmospheres, V in Liters, n in number of moles, and T in kelvins. In SI units, R is expressed as 8.315 J / mol K. If you are trying to figure out how the product of P and V could get you a value of 8.315 J, you need to remember that in SI units Pressure is expressed in N / m2 and Volume is expressed in m3. When you multiply the two together you get the N m. The N m is the same as the joule. (Work = Force x distance)]

[To find the value for Boltzman's constant, k, you would need to take the value for R expressed in SI units, which is a value expressed per mole and divide it by Avogadro's number to get the value per individual molecule. Thus k is equal to 1.38 x 10-23.]

Real Gases: At low temperatures and high pressures real gases deviate from the laws we are in the process of studying. As long as the intermolecular forces are having little impact on the motion of the molecules and the collisions are relatively elastic, real gases behave pretty much the way that these relationships suggest. The problem occurs as gases cool down approaching their condensation temperatures and their low kinetic energies allow for intermolecular forces to have a significant effect and when high pressures (high densities) force the molecules very close together and allow for intermolecular forces to also have a significant effect.

[The critical temperature of a substance is the temperature to which a gaseous substance must be cooled before it can be liquified by pressure. The critical pressure of a substance is the pressure needed to liquify a gaseous substance that is at its critical temperature. At temperatures above the critical temperature a substance is usually called a gas. At temperatures below the critical temperature it is usually called a vapor, assuming it has not in liquid or solid state. The triple point of a substance is an exact combination of a single temperature and pressure measurement where all three phases of the substance can exist simultaneously in a state of physical equilibrium.]

Vocabulary: gas, temperature, standard temperature, volume, standard volume, pressure, atmospheric pressure, standard atmospheric pressure, STP, mole, density, Pascal (the unit), Atmosphere (the unit), Liter, barometer, manometer, elastic collision, Boyle’s Law, Charles’ Law, interpolation, extrapolation, Combined gas law, Ideal Gas Law, universal gas constant, Boltzmann constant, real gas, Avogadro’s number

Skills to be learned:

Solve Pressure Conversion Problems

Solve Boyle's Law Problems

Solve Charles' Law Problems

Solve Gay-Lussac's Law Problems

Solve Combined Gas Law Problems

Solve Ideal Gas Law Problems

Assignments:

Textbook: NA, Sources will be announced

WB Exercises: PS#13-1, PS#13-2, PS#13-3 and PS#13-4

Activities: TBA

Resourses:

This Handout and the Overhead and Board Notes discussed in class

WB Lessons and Problem Sets

- “Gas Laws”

 / Gas Laws